Association Equilibrium of Methylene Blue by Spectral Titration and Chemometrics Analysis: A...

Communication

Association Equilibrium of Methylene Blue by Spectral Titration and

Chemometrics Analysis: A Thermodynamic Study

Jahan B. Ghasemia,* and M. Miladib

aChemistry Department, Faculty of Sciences, K. N. Toosi University of Technology, Tehran, IranbChemistry Department, Razi University, Kermanshah, Iran

The monomer-dimer equilibrium of methylene blue (MB, Scheme I) has been investigated by means

of UV-Visible spectroscopy in aqueous solutions. The self aggregation of MB in water has been investi-

gated by recording absorption spectra in the wavelength range of 450-750 nm, and in different ionic

strengths using concentrated KCl solutions in the temperature range of 20-90 �C. Chemometrics analysis

of the spectral data gave a dimerization constant, individual spectra of the monomer and dimer forms of

the dye molecule. The quantitative analysis of the data of the undefined mixture was carried out by simul-

taneous resolution of the overlapping spectral bands in the whole set of absorption spectra. The dimeriza-

tion constants of MB determined by mathematical deconvolution of the thermometric spectral titration

data show dependency on temperature variations. The concentration range of MB was 6.00 � 10-5-3.00 �10-4 M. Utilizing the van’t Hoff relation, which describes the dependence of the equilibrium constant on

temperature, the thermodynamics parameters �H� and �S� of the aggregation process were determined.

The compensation effect was verified by the thermodynamics results of the dimerization process of the

dye.

Keywords: Thermodynamics; Dimerization; Chemometrics; Dye; Methylene blue; Titration;

Ionic strength.

1. INTRODUCTION

The aggregation of dyes, drugs, surfactants, etc. in

aqueous solutions is of extreme importance in biological,

colloid, surface, textile, photographic and analytical chem-

istry.1 In general, a wide variety of applications of pheno-

thiazine dyes have been reported, for example, as sensi-

tizers in solar energy conversion,2 redox mediators in cata-

lytic oxidation reactions,3 active species in electrochro-

mism4 and dye lasers,5 ingredients in pharmaceutical prep-

arations,6 candidates for cancer therapy by intercalating be-

tween DNA base layers7 as sensors or for probing chemical

properties at interfaces, especially in biochemistry and mo-

lecular biology.8 However, all of these applications are of-

ten complicated due to the dimerization of dye molecules in

aqueous media such as the great decrease in light sensitiv-

ity,9 which results from increased inner conversion of the

dimer exciter state. In order to determine the mode of ag-

gregation, the aggregation constant in equilibrium and the

aggregation number, the aggregation of dyes has been in-

vestigated by a variety of methods, viz. polarography,10,11

conductometry12 UV-Vis spectrophotometry,13-19 NMR,20-22

light scattering23 and electrolytic effect24 measurements.

The nature of the self-association of dyes in aqueous

solutions, aside from its intrinsic interest, is important in

the understanding and interpretation of a great variety of

problems, such as dyeing of fibers, tissue staining in biol-

ogy, spectral change and energy transfer studies, adsorp-

tion, and photography. Dye association is also one of the

simplest examples of “stacking” interactions. Many dyes

show appreciable association at concentrations as low as

10-6-10-4 M, and the qualitative evidence from many stud-

ies suggests that a series of multimers are formed.25

Journal of the Chinese Chemical Society, 2009, 56, 459-468 459

* Corresponding author. Tel: +0098-21-22853306; Fax: +0098-21-22850266; E-mail: [email protected]

S

N

NNCl

-

Scheme I

Methylene blue (MB), one of the most commonly

used thiazine dyes, is known for its pronounced methach-

romatic behavior and aggregation in various solutions.26-27

The fact that the visible absorption spectra of aqueous MB

solutions do not obey Beer’s law has been ascribed to MB

molecular aggregation,26-27 which is influenced by the con-

centration of the dye, the dielectric constant of the solvent,

the addition of salt, and so on. Most attempts to study this

aggregation quantitatively have been focused on dimeriza-

tion.26 Deciphering solution complexes is one of the most

challenging problems in analytical chemistry, because the

varying species exist in equilibria and cannot be isolated.

The amounts of the various species are functions of the

controlling equilibria. As such, their concentrations are

sensitive to solvent composition, temperature, reagent con-

centrations, pH, etc. Although dyes are very individualistic

in structure and of course behavior, certain broad rules are

well established regarding aggregation in general. It may

increase with an increase of dye concentration or ionic

strengths; it will decrease with raising the temperature or

adding organic solvents; addition to the dye structure of

ionic soubilizing groups will decrease aggregation, where-

as the inclusion of long alkyl chains increases aggregation

because of a higher hydrophobic interaction in solution.

Absorption UV-vis spectroscopy is one of the most

suitable methods for quantitatively studying the aggrega-

tion phenomena of dyes as a function of concentration. In

the commonly used concentration range (10-3 to 10-6 M) the

main equilibrium is a monomer-dimer reaction. In this

work we used some physical constraints to determine the

dimeric concentration of MB in pure water and at different

ionic strengths. Data analysis was carried out by the DATAN

package that was developed by the Kubista groups.28-36 The

theory and application of the physical constraints method

were discussed by Kubista et al. in several papers.28-38 How-

ever, the general principal will be outlined here briefly. The

results of the DATAN package were compared to the re-

sults of a single wavelength or classical regression method

of the absorbance data which is written in MATLAB.

The absorption spectra are digitized and arranged as

rows in a data matrix A. Matrix A is then decomposed into

an orthogonal basis set using, for example, the NIPLAS

routine:21

A TP E TP� � � � � � �� t pi i

i

r

1

(1)

where ti are orthogonal target vectors and pi� the orthogonal

projection vectors, E the error matrix, and r the number of

spectroscopically distinguishable components, which is

two in this case. Assuming linear response the recorded

spectra are also linear components:

A CV E CV� � � �� ci i

i

r

1

(2)

where ci are vectors containing the component concentra-

tions at different temperatures. Eqs. (3) and (4) are related

by a rotation:

C = TR-1 (3)

V = RP' (4)

where R is r � r rotation matrix, which for a two-component

system has the element:

R �

��

��

r r

r r

11 12

21 22

and R� �

�

�

�

��

��

1

11 22 12 21

22 12

21 11

1

r r r r

r r

r r(5)

Two constraints are used to determine three of the elements

in R. The first is the spectrum of the monomer, which is

measured separately, and the second is the constant total

concentration of the dye:

cX(T) + 2cX2(T) = ctot (6)

Matrix R can now be described by a single scalar r21,

and other factors that are determined by the constraints.

The value of r21 determines the dimer spectrum and the

monomer concentration profiles. Although a value of r21

produces a mathematically acceptable solution, reasonable

results, in terms of spectral intensities and nonnegative

concentrations and spectral responses, are obtained in a rel-

atively narrow range of r21 values. Still, the range is, in gen-

eral, too large for a quantitative analysis. The final con-

straint, which produces a unique solution, is the thermody-

namic relation between temperature and the equilibrium

constant. The component concentrations are related by the

law of mass action39

K Tc T c

c T cD

x

x

( )( ) /

( ( ) / )� 2

2

�

�

(7)

where c� = 1 mol/dm3. Assuming that the dimerization con-

stant KD(T) depends on temperature according to the van’t

Hoff equation,39

460 J. Chin. Chem. Soc., Vol. 56, No. 3, 2009 Ghasemi and Miladi

d K T

d TH RDln ( )

( / )/

1� �� (8)

where �H� is the molar enthalpy change, R = 8.314 J mol-1

K-1 is the universal gas constant, and T the Kelvin tempera-

ture. A linear regression of equilibrium constant with re-

spect to 1/T is then performed, which determines a trial

enthalpy change of the reaction. Several studies based on

the application of this method to evaluate spectrometric

data have been reported.28-41

2. EXPERIMENTAL

2.1. Artificial Data Set

The artificial data sets were generated based on Beer-

Lambert’s law. Concentration profiles are constructed ac-

cording to mass-balance equations and the spectrum of

each species constructed by using a Gaussian formula with

respect to the physico-chemical behavior of the system

under study. To evaluate the robustness of the proposed

method, different random noise levels were superimposed

on each absorbance reading. The spectra were simulated in

the wavelength range of 540-700 nm and the temperature

range is 20-90 �C (5 �C intervals) with initial guesses of

enthalpy and entropy values. The simulated data series

have been refined by using the DATAN program.

2.2. Real Data Set

2.2.1. Instrumentation and Software

Absorption spectra were measured on a CARY 100

UV-Visible Spectrophotometer (Varian) equipped with a 1

mm quartz cell with a temperature controller and a 1 nm

bandwidth spectral bandpass, and were digitized with five

data points per nanometer. The cuvettes were treated with

repel-silane prior to measurements to avoid dye adsorp-

tion.

All absorption spectra in the wavelength range of

540-700 nm were transferred (in ASCII format) to an

Athlon 2000 XP computer for analysis by MATLAB (Math-

works, Version 6.5) and DATAN package ver 3.1.42

2.2.2. Chemical Reagents

All the chemicals used were of analytical reagent

grade. Subboiling, distilled water was used throughout.

MB (for microscopy grade) was purchased from Fluka and

used without additional purification. A stock solution of

MB (1.00 � 10-3 M) was prepared. In all experiments the

ionic strength was adjusted using KCl (Fluka).

3. RESULTS AND DISCUSSION

3.1. Absorption spectra

Two sets of simulated and experimental absorption

spectra were prepared to examine the ability of the DATAN

package in determination of dimerization constants. The

first set obtained was based on Beer-Lambert’s law and us-

ing a Gaussian formula with specifications mentioned in

the experimental section. The quantity of added noise to the

generated absorption spectra is random. The sample three

dimensional plot of the generated absorption spectra loaded

with random noise is shown in Fig. 1. The wavelength and

temperature range of the spectra were 600-700 nm and

20-90 �C temperature units, respectively. The second sets

are experimental data of MB obtained at different total dye

concentrations, and ionic strengths were recorded in the

wavelength range of 540-700 nm. The typical absorption

spectra of the MB in aqueous solution are shown in Fig. 2.

3.2. Determination the dimerization constant of simu-

lated and experimental data set

As expected, by increasing the temperature and de-

creasing the concentration, the monomer form would be

predominant over the dimer form. So, it is wise to choose

the spectrum of the dye at the highest temperature and at the

Chemometric Study of Methylene Blue Association J. Chin. Chem. Soc., Vol. 56, No. 3, 2009 461

Fig. 1. The simulated absorption spectra of methylene

blue loaded with 2% noise. (a: 6.00 � 10-5, b:

9.00 � 10-5, c: 3.00 � 10-4 M) with 5 �C intervals

from 20-90 �C.

lowest concentration as an initial estimate for the monomer

in subsequent calculations.

According to Equations (1)-(8), the DATAN program

starts with a trial value of r21, at a predefined interval, and

iterates all the calculation steps. The iteration stops when

all r21 values in the preset interval are tested. The KD, dimer

spectrum, �S� and �H�, corresponding to a minimum value

of the �2 statistics, are selected as the final results. The �2 is

the sum of squared residuals29 and generally used as a

goodness of fit criterion and its value indicates the predict-

ability of the model, i.e., how well the monomer spectrum

and r21 are determined. The general formula of the �2 is:

� 2 2

1

� �� ( ) /exp expA A Acalc

i

n

where Aexp is the expected value and Acalc the value calcu-

lated from the experimental data over n data points.

By a rising the temperature, an absorption peak, for

MB, around 664 nm grows and an absorption shoulder

around 610 nm decreases (Fig. 2). We analyzed the tem-

perature titrations assuming monomer-dimer, monomer-

dimer-trimer and even some models including higher order

aggregates. It was found that a monomer-dimer model most

adequately describes the data in these ranges of dye con-

centrations. The presence of exactly two species is also evi-

denced by the appearance of an isosbestic point at 620 nm

(Fig. 2).

The dimerization constants of the simulated absorp-

tion spectra loaded with noise are calculated by the DATAN

program. The dimerization constant at 25 �C and different

concentrations are shown in Table 1. The general outputs of

the program involve a linear van’t Hoff plot, the spectral re-

sponses of the monomer and dimer species, their concen-

tration as a function of temperature (Fig. 3) and changes in

the �H� and �S� of the reaction (Table 2).

The dimerization constants (KD) were calculated at

different temperatures and dye concentrations in pure wa-

ter. As expected, KD decreased with increasing tempera-

ture, while it is virtually independent of total dye concen-

tration. The dimerization constant at 25 �C and at different

concentrations and thermodynamic parameters of the di-

merization reaction are listed in Table 3. It is clear from the


Fig. 2. Experimental absorption spectra of MB in wa-

ter (a: 6.00 � 10-5, b: 9.00 � 10-5, c: 3.00 � 10-4

M) with 5 �C intervals from 20-90 �C.

Fig. 3. Linear van’t Hoff plots, molar ratios as a func-

tion of temperature and spectral profiles of the

monomer and dimer species for simulated data

of MB, 9 � 10-5, with and without noise (sub-

scribes 1 and 2 for letters a to c denote absence

and the presence of noise, respectively).

result that the obtained dimerization constants obtained are

the same within the margin of the experimental errors.

From the dependence of log KD on 1/T (Fig. 4), �S�and �H� values were determined; the �H� values range

from -41.8 KJ mol-1 to -49.3 KJ mol-1 with mean -46.84 KJ

mol-1 while �S� ranges from -62 to -85 J mol-1 K-1 with

mean -76 J mol-1 K-1. As described, the above dimerization

is presumed to be the dominant form of aggregation in ap-

plied concentration ranges in aqueous MB. This is corrobo-

rated by the constancy of the apparent enthalpy of associa-

tion. In general, the extent of aggregation depends recip-

rocally on the temperature of the solution and is fully re-


Table 1. Dimeric constant (KD) value for the simulated data loaded with noise at different

concentrations of MB

Concentration of MB

Data set 6.00 � 10-5 M 9.00 � 10-5 M 3.00 � 10-4 M

0% Noise LogKD (25� C) 21.9 � 103 19.4 � 103 13.2 � 103

2% Noise LogKD (25� C) 19.9 � 103 19.6 � 103 13.1 � 103

Table 2. Thermodynamic parameter values of MB for simulated

data loaded with noise at different concentrations

Data set Concentration �H� (KJ mol-1) �S� (J mol-1 K-1)

0% Noise 6.00 � 10-5 M -49.2 -82

9.00 � 10-5 M -49.4 -84

3.00 � 10-4 M -41.8 -61

2% Noise 6.00 � 10-5 M -48.4 -79

9.00 � 10-5 M -49.8 -85

3.00 � 10-4 M -41.2 -59

Table 3. Dimeric constant (KD) and thermodynamic parameter

values for the experimental data of MB at different

concentrations in pure water

Concentration

6.00 � 10-5 M 9.00 � 10-5 M 3.00 � 10-4 M

LogKD (25 �C) 4.31 4.26 4.13

�H� (KJ mol-1) -49.2 -49.4 -41.7

�S� (J mol-1 K-1) -82 -84 -61

Fig. 4. The van’t Hoff plot at different concentrations

of MB for experimental data in water (a: 6.00 �10-5, b: 9.00 � 10-5, c: 3.00 � 10-4 M).

Fig. 5. Molar ratio of MB dye monomer (o) and dimer

(�), compared to molar ratios predicted by the

temperature dependence of the equilibrium

constant (shown as solid line) at different con-

centrations of MB dye in water (a: 6.00 � 10-5,

b: 9.00 � 10-5, c: 3.00 � 10-4 M).

versible. The observed relationship between entropy and

enthalpy reflects an electronic nature of the dimerization

phenomenon of MB. The relative dependence of the con-

centrations of the monomer and dimer of MB on the tem-

perature in different concentrations are shown diagram-

matically in Fig. 5. The calculated absorption spectra of

MB in monomer and dimer forms are shown in Fig. 6.

For studying the effect of ionic strength on dimeriza-

tion of MB using potassium chloride, the dimerization was

investigated at different ionic strengths. Spectra of MB (5 �10-5 M) at different ionic strengths in the temperature range

of 20-90 �C with 5 �C intervals are shown in Fig. 7. Hydro-

phobic bonding, hydrophobic forces, and electrostatic in-

teractions may be all considered important for dimeriza-

tion. What effect we expected from the increasing of the

ionic strength on the dimerization constants according to

the extended Debye-Huckel equation,43-44 totally depends

on the relative charge of the dimer species with respect to

the two monomer moieties. As can be seen from the data

obtained at different ionic strengths (Table 4), the increas-

ing of the ionic strength results in an increase of the dime-

rization constants. The dimeric constant at 25 �C and ther-

modynamic parameters values of MB at different concen-

trations of ionic strengths are listed in Table 4.

One of the most interesting points of the change of the

ionic strength on the dimerization reactions of the MB is

the spectral changing of the dimer form. The dimer spectra

of MB show enhancement of the spectral band with �max’s

around 664 nm as compared with those in water. Patil et

al.45 reported a similar spectral change from the effect of

the addition of some solutes to the aqueous solution of MB.

They showed that these spectral variations depend on the

angle between the two dye molecule planes which in turn

depend on the concentration of the inert solutes. The de-

crease in dimer formation constant values with an increase

in the concentration of each on inert salts also indicates the

decreased tendency of MB molecules to undergo aggrega-

tion. The random variations in the formation constants by

changing ionic strength may be returned to the presence of

the un-accounted interactions such as anion–cation attrac-

tive type interactions, etc., in addition to monomer-dimer

equilibrium.

Despite the abovementioned variations which have a

deterministic effect on the thermodynamics parameters of

dimerization at MB, the T�S versus �H� plot, Fig. 8 shows

a fairly good linear correlation indicating the existence of

enthalpy-entropy compensation in dimeric reactions. The

linear correlation observed between T�S and �H� values

can be expressed as T�S = T�S� + � �H� with T�S� =

17.54 KJ mol-1, � = 0.82 (R2 = 0.9711) for thermodynamics

data of the dimerization process of MB. The same trends


Fig. 6. Calculated absorption spectra of MB dye

monomer (—) and dimer (---) at different con-

centrations in water (a: 6.00 � 10-5, b: 9.00 �10-5, c: 3.00 � 10-4 M).

Table 4. Dimeric constant (KD) and thermodynamic parameters values of methylene blue dye

(5 � 10-5 M) at different ionic strengths by potassium chloride

Concentration of KCl (M)

0.5 1 1.4 1.5 1.6 1.8 2.2

LogKD (25 �C) 5.09 5.15 5.22 5.33 4.38 5.25 5.46

�H� (KJ mol-1) -63.4 -63.6 -55.5 -62 -43.2 -76.8 -157.3

�S� (J mol-1 K-1) -117 -116 -87 -107 -52 -157 -142

are reported from the thermodynamics study of the reac-

tions largely accompanying changes in electrostatic inter-

actions during the association reactions or host-guest phe-

nomena.46-49

The result suggests that the entropic effect consists of

two components. The first component T�S� is independent

of enthalpy change and the second is proportional to it. The

proportionality constant � might be considered as a quanti-

tative measure of the enthalpy-entropy compensation. For

MB, � = 0.82, only about 18% of the increase in �H con-

tributed to dimeric stability. The close-to-zero intercept of

T�S� KJ mol-1 reveals that the dimerization process here in

nature can be classified as enthalpy driven. These results

can be supported by the fact that the dimerization constant

is increased by the increase of the ionic strengths of the me-

dium which in turn show the increasing of the charge of the

dimer that are more solvated by the solvents molecules, and

entropic change would have less positive values. Another

point that appears to be true about Fig. 8 which indicates

the compensation effect is that the linear plot shows that a

single mechanism is most likely to dominate the range of

ionic strengths investigated. The ionic strength will affect

the solubility such as salt-in and salt-out effects. Recently

there have been some reports on the kinetic and thermody-


(Continued)

namic study on adsorption and desorption of MB on differ-

ent activated charcoals.50-53 These papers report that the as-

sociation of the MB have a pronounced effect on the ad-

sorption desorption phenomena.

4. CONCLUSION

In this study we reported, for the first time to our

knowledge, dimerization constants, concentration profiles,

and spectral responses of monomer and dimers obtained by

computer refinement of temperature photometric titrations.

We also report a thermodynamic study of the dimerization


Fig. 7. Experimental traces (left) absorption spectra of MB (5.00 � 10-5 M) with 5� interval between 20-90 �C at different

ionic strengths (a: 0.5, b: 1, c: 1.4, d: 1.5, e: 1.6, f: 1.8 M of KCL). The right side indicates monomer (—) and dimer

(---) of MB at corresponding concentrations and ionic strengths.

Fig. 8. Plot of T�S vs. �H� for dimerization of MB of

different concentrations in various ionic strengths

media.

equilibrium of MB in different ionic strengths. The thermo-

dynamic parameters of enthalpy and entropy of dimeriza-

tion reactions were calculated from the dependence of

dimeric constant on the temperature (van’t Hoff equation).

The relationship between entropy and enthalpy reflected

the electrostatic nature of the dimerization phenomenon,

which can be quantitatively expressed in the relation of

T�S�-�H� and also show that the dimerization reactions, in

this case, are classified as enthalpy driven category reac-

tions. The obtained data show the aqueous solutions of MB

are complex systems. So we suggest applications of more

powerful data handling methods such as global analysis to

overcome these complexities.

Received December 31, 2008.

REFERENCES

1. Dakiky, M.; Nemcova, I. Dyes Pigm. 1999, 40, 141-150.

2. Kamat, P. V.; Lichtin, N. N. J. Phys. Chem. 1981, 85, 814-

818.

3. Ye, J.; Baldwin, P. R. Anal. Chem. 1988, 60, 2263-2268.

4. Ohtani, M.; Kuwabata, S.; Yoneyama, H. J. Electroanal.

Chem. 1997, 422, 45-54.

5. Braslavaky, S.; Gensch, T. J. Phys. Chem. B. 1997, 101,

101-108.

6. Foncer, G. J. S.; Reej, R. C.; Devonshire, R. Photochem.

Photobiol. 1990, 52, 489-495.

7. Tuite, E.; Norden, B. J. Am. Chem. Soc. 1994, 116, 7548-

7556.

8. Czìmerová, A.; Bujdák, J.; Gáplovský, A. Coll. Surf. A:

Physicochem. Eng. Aspects 2004, 243, 89-96.

9. Elena, R.; Giulo, J. Rev. Chem. Intermed. 1998, 10, 260-

265.

10. Iyer, S.; Singh, G. J. Soc. Dye. Colo. 1973, 89, 128-134.

11. Duff, D. G.; Kirkwod, D. J.; Stevenson, D. M. J. Soc. Dye.

Colo. 1977, 93, 303-309.

12. Kendrick, K. L.; Gilikeson, W. R. J. Sol. Chem. 1987, 16,

257-263.

13. Monahan, A. R.; Blossey, F. J. Phys. Chem. 1970, 74,

4014-4021.

14. Monahan, A. R.; Germano, N. J.; Blossey, D. F. J. Phys.

Chem. 1971, 75, 1227-1233.

15. Monahan, A. R.; Deluca, A. F.; Ward, A. T. J. Org. Chem.

1971, 36, 3838-3842.

16. Tull, A. G. J. Soc. Dye. Colo. 1973, 89, 132-141.

17. Ott, R.; Widmer, U.; Zolinger, H. J. Soc. Dye. Colo. 1975,

91, 330-337.

18. Hsieh, B. R.; Desilets, D.; Kazmaier, P. M. Dyes Pigm. 1990,

14, 165-189.

19. Hamada, K.; Nonogaki, H.; Fukushima, Y.; Munkhbat, B.;

Mistsuishi, M. Dyes Pigm. 1991, 16, 111-118.

20. Hamada, K.; Nishizawa, M.; Kitsuishi, M. Dyes Pigm. 1991,

16, 165-171.

21. Hamada, K.; Take, S.; Lijima, T. J. Chem. Soc, Farad.

Trans. 1986, 82, 3141-3145.

22. Asakura, T.; Ishida, M. J. Coll. Inter. Sci. 1989, 130, 184-

189.

23. Dalyner, A.; Flowers, A.; Pailithorpe, M. J. Coll. Inter. Sci.

1980, 74, 71-79.

24. Liska, M.; Bartos, L.; Valasek J. Chem. Pap. 1989, 43,

303-308.

25. Mukerjee, P.; Ghosh, A. K. J. Am. Chem. Soc. 1970, 92,

6403-6407.

26. Bergmann, K.; O’Konski, C. T. J. Phys. Chem. 1963, 67,

2169-2177.

27. Braswell, E. J. Phys. Chem. 1967, 72, 2477-2483.

28. Kubista, M.; Sjoback, R.; Nygren, J. Anal. Chim. Acta 1995,

302, 121-125.

29. Kubista, M.; Nygren, J.; Elbergali, A.; Sjoback, R. Crit. Rev.

Anal. Chem. 1999, 29, 1-5.

30. Kubista, M.; Sjoback, R.; Albinsson, B. Anal. Chem. 1993,

65, 994-998.

31. Scarminio, I.; Kubista, M. Anal. Chem. 1993, 65, 409-416.

32. Elbergali, A.; Nygren, J.; Kubista, M. Anal. Chim. Acta

1999, 379, 143-158.

33. Nygren, J.; Andrade, J. M.; Kubista, M. Anal. Chem. 1996,

68, 1706-1710.

34. Svanvik, N.; Nygren, J.; Westman, G.; Kubista, M. J. Am.

Chem. Soc. 2001, 123, 803-809.

35. Nygren, J.; Svanvik, N.; Kubista, M. Biopolym. 1998, 46,

39-51.

36. Nygren, J.; Elbergali, A.; Kubista, M. Anal. Chem. 1998, 70,

4841-4846.

37. Ghasemi, J.; Niazi, A.; Kubista, M.; Elbergali, A. Anal.

Chim. Acta 2002, 455, 335-342.

38. Ghasemi, J.; Ahmadi, Sh.; Kubista, M.; Forootan, A. J.

Chem. Eng. Data 2003, 48, 1178-1182.

39. Levine, L. V. Physical Chemistry; McGraw-Hill: New York,

1988.

40. Antonov, L.; Gergov, G.; Petrov, V.; Kubista, M.; Nygren, J.

Talanta 1999, 49, 99-106.

41. Ghasemi, J.; Niazi, A.; Westman, G.; Kubista, M. Talanta

2004, 62, 835-841.

42. http://www.multid.se (Accessed May 22, 2009)

43. Debye, P.; Huckel, E. Phys. Z. 1923, 24, 165-172.

44. Debye, P.; Huckel, E. Phys. Z. 1923, 24, 305-311.


45. Patil, K.; Pawar, R.; Talap, P. Phys. Chem. Chem. Phys.

2000, 2, 4313-4317.

46. Laitinen, H. A.; Harris, W. E. Chemical Analysis; McGraw-

Hill: London, 1975.

47. Inoue, Y.; Hakushi, T. J Chem. Soc. Perkin Trans. II 1985,

935-939.

48. Ghasemi, J.; Shamsipur, M. J. Coord. Chem. 1995, 36,

183-194.

49. Ghasemi, J.; Meibody, Z. A. J. Sci. Iran 1999, 32, 158-165.

50. Ghasemi, J.; Assadpour, S. J. Chem. Thermodyn. 2007, 39,

967-971.

51. Bangash, F. K.; Manaf, A. J. Chin. Chem. Soc. 2005, 52,

489-494.

52. Wang, W. K. J. Chin. Chem. Soc. 2003, 50, 403-406.

53. Wang, W. K.; Zhou, W. Z.; Huang, W. L. J. Chin. Chem. Soc.

2003, 49, 999-1002.


Association Equilibrium of Methylene Blue by Spectral Titration and Chemometrics Analysis: A...

Documents

Transcript of Association Equilibrium of Methylene Blue by Spectral Titration and Chemometrics Analysis: A...